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M. Mateo, Patrick Lambert, S. Tétard, M. Castonguay, B. Ernande, Hilaire Drouineau
To cite this version:
M. Mateo, Patrick Lambert, S. Tétard, M. Castonguay, B. Ernande, et al.. Cause or consequence?
Exploring the role of phenotypic plasticity and genetic polymorphism in the emergence of phenotypic spatial patterns of the European eel. Canadian Journal of Fisheries and Aquatic Sciences, NRC Research Press, 2017, 74 (7), pp.987-999. �10.1139/cjfas-2016-0214�. �hal-01548904�
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Cause or consequence? Exploring the role of phenotypic plasticity and genetic polymorphism in the1
emergence of phenotypic spatial patterns of the European eel
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Authors:
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Maria MATEO (corresponding author)
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o Affiliations: Irstea, UR EABX Ecosystèmes aquatiques et changements globaux, HYNES
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Irstea – EDF R&D
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o Address: 50 avenue du Verdun, 33 612 Cestas, France
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o Tel: +33 (0)5 57 89 09 98
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o Email: maria.mateo@irstea.fr
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Patrick LAMBERT
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o Affiliations: Irstea, UR EABX Ecosystèmes aquatiques et changements globaux, HYNES
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Irstea – EDF R&D
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o Address: 50 avenue du Verdun, 33 612 Cestas, France
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o Email: patrick.lambert@irstea.fr
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Stéphane TETARD
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o Affiliations: EDF R&D, HYNES Irstea – EDF R&D, Laboratoire National d’Hydraulique et
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Environnement
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o Address: 6 quai Watier, 78 401 Chatou, France
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o Email: stephane.tetard@edf.fr
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Martin CASTONGUAY
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o Affiliations: Ministère des Pêches et des Océans, Institut Maurice-Lamontagne
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o Address: C.P. 1000, 850, route de la Mer, Mont-Joli, QC G5H 3Z4, Canada
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o Email: Martin.Castonguay@dfo-mpo.gc.ca
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Bruno ERNANDE
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o Affiliations: IFREMER, Laboratoire Ressources Halieutiques de Boulogne
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o Address: 150 Quai Gambetta, BP 699, 62 321 Boulogne-sur-Mer, France27
o Email: bruno.ernande@ifremer.fr
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Hilaire DROUINEAU
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o Affiliations: Irstea, UR EABX Ecosystèmes aquatiques et changements globaux, HYNES
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Irstea – EDF R&D
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o Address: 50 avenue du Verdun, 33 612 Cestas, France
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o Email: hilaire.drouineau@irstea.fr
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3
1 Abstract
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The European eel (Anguilla anguilla), and generally, temperate eels, are relevant species for
35
studying adaptive mechanisms to environmental variability because of their large distribution areas
36
and their limited capacity of local adaptation. In this context, GenEveel, an individual-based
37
optimization model, was developed to explore the role of adaptive phenotypic plasticity and genetic-
38
dependent habitat selection, in the emergence of observed spatial life-history traits patterns for eels.
39
Results suggest that an interaction of genetically and environmentally controlled growth may be the
40
basis for genotype-dependent habitat selection, whereas plasticity plays a role in changes in life-
41
history traits and demographic attributes. Therefore, this suggests that those mechanisms are
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responses to address environmental heterogeneity. Moreover, this brings new elements to explain
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the different life strategies of males and females. A sensitivity analysis showed that the parameters
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associated with the optimization of fitness and growth genotype were crucial in reproducing the
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spatial life-history patterns. Finally, it raises the question of the impact of anthropogenic pressures
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that can cause direct mortalities but also modify demographic traits, and act as a selection pressure.
47 48
Keywords: phenotypic plasticity, Anguilla anguilla, genetic polymorphism, life history theory,
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modeling
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4
2 Introduction
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Life-history theory posits that the schedule and duration of life-history traits are the result of
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natural selection to optimize individual fitness (Clark 1993; Giske et al. 1998). Optimal solutions
53
greatly depend on environmental conditions, and consequently, living organisms have developed
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different adaptive mechanisms to address environmental variability. Among them, local adaptation
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theory posits that natural selection favors the most well adapted genotypes in each type of
56
environment. In a context of limited genetic exchange between environments, this may lead to
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isolation and speciation (Williams 1996; Kawecki and Ebert 2004). Phenotypic plasticity might also be
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an adaptive response to an heterogeneous environment (Levins 1963; Gotthard and Nylin 1995;
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Pigliucci 2005). Phenotypic plasticity refers to the possibility of a genotype to produce different
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phenotypes depending on environmental conditions. In some cases, increases in fitness occur
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because of plastic phenotypes compared to non-plastic ones, and that consequently, phenotypic
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plasticity may be selected by natural selection (Schlichting 1986; Sultan 1987; Travis 1994).
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Adaptation to environment heterogeneity is a key issue for temperate anguilids, Anguilla
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anguilla, A. japonica, A. rostrata, three catadromous species that display remarkable similarities in
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their life-history traits (Daverat et al. 2006; Edeline 2007). The European eel (A. anguilla) is widely
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distributed from Norway to Morocco, grows in contrasting environments, and displays considerable
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phenotypic variation. The species displays a complex life cycle: reproduction takes place in the
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Sargasso Sea, larvae (or leptocephali) are transported by ocean currents to European and North
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African waters, where they experience their first metamorphosis to become glass eels. These
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juveniles colonize continental waters and undergo progressive pigmentation changes to become
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yellow eels. The growth phase lasts between two and 20 years depending upon the region and sex of
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the eels (Vollestad 1992). At the end of this stage, yellow eels metamorphose again into silver eels,
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which mature during the migration to their spawning area in the Sargasso Sea. The population is
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panmictic, resulting in a homogeneous population, from a genetic viewpoint (Palm et al. 2009; Als et
75
5
al. 2011; Côté et al. 2013). This panmixia combined with a long and passive larval drift limit the76
possibility of adaptation to local environments. However, spatial patterns of different life traits,
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including growth rate (Daverat et al. 2012; Geffroy and Bardonnet 2012), sex (Helfman et al. 1987;
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Tesch 2003; Davey and Jellyman 2005), length at maturity (Vollestad 1992; Oliveira 1999), and habitat
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use (De Leo and Gatto 1995; Daverat et al. 2006; Edeline 2007) are observed and correlated with
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environmental patterns.
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Growth rates greatly vary depending on latitude, temperature, sex (Helfman et al. 1987) but
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also on habitat characteristics (Cairns et al. 2009). Indeed, eel can settle in a wide range of habitats
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(De Leo and Gatto 1995; Daverat et al. 2006; Geffroy and Bardonnet 2012) and faster growth is
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observed in brackish waters than in freshwater (Daverat et al. 2012). Slower growth in freshwater
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habitats is sometimes assumed to be compensated for by lower mortalities and Edeline (2007)
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suggested that habitat choice could be the result of a conditional evolutionary stable strategy.
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However, Cairns et al. (2009) questioned this assumption because they did not observe strong
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variation in mortality rates between habitats. Spatial patterns were also observed with respect to sex
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ratios, with female biased sex ratios in the upper part of river catchments (Tesch 2003) and in the
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northern part of the distribution range (Helfman et al. 1987; Davey and Jellyman 2005). However, sex
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is not determined at birth but is determined by environmental factors (Oliveira 2001; Davey and
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Jellyman 2005; Geffroy and Bardonnet 2012). Population density also plays a role in this mechanism:
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males are favored at high densities, whereas low densities favor females (Tesch 2003). This is
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important because males and females have different life-history strategies (Helfman et al. 1987). The
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reproductive success of a male does not vary with body size, and consequently, males are assumed
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to follow a time-minimizing strategy, leaving continental waters as soon as they have enough energy
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to migrate to the spawning grounds (Vollestad 1992). However, a female’s reproductive success is
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constrained by a trade-off between fecundity, which increases with length, and survival, which
99
decreases with length. Consequently, females are assumed to adopt a size-maximizing strategy
100
6
(Helfman et al. 1987). Strong differences in female length at silvering were observed among habitats101
and latitudes (Oliveira 1999).
102
Because local adaptation is impossible, this raises two questions: (i) are those life-history
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trait patterns resulting from an adaptive response to environmental heterogeneity, and (ii) which
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adaptation mechanisms have been selected. Despite panmixia, previous researchers (Gagnaire et al.
105
2012; Ulrik et al. 2014; Pavey et al. 2015) have detected genetic differences correlated with
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environmental gradients and assumed that those differences were reshuffled at each generation.
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Common garden experiments have been used to test the respective contributions of genetic and
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plastic mechanisms on phenotypic differences observed in glass eels found in distinct locations. The
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results revealed genetic patterns related to geographic zones in American eels, whereas individual
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growth rates had a genetic basis and could be sex-dependent (Côté et al. 2009, 2014, 2015). Building
111
on this, Boivin et al. (2015) studied the influence of salinity preferences and geographic origin on
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habitat selection and growth in American eels, demonstrating genetic-based differences for growth
113
between glass eels from different origins. However, these experiments also confirmed the
114
contribution of phenotypic plasticity that allowed individuals to develop quick and effective
115
responses to environmental variability (Hutchings et al. 2007). Several traits have been proposed as
116
plastic: growth habitats (Daverat et al. 2006; Edeline 2007), growth rates (Geffroy and Bardonnet
117
2012), and length at silvering (Vollestad 1992). Understanding the adaptive mechanisms that explain
118
this diversity is crucial to environmental conservation and management (Brodersen and Seehausen
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2014).
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As a result of a decline observed since the 1980s, the European eel is now listed as critically
121
endangered in the IUCN Red List (Jacoby and Gollock 2014) and the European Commission enforced a
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European Regulation, which requires a reduction in all sources of anthropogenic mortality (obstacles,
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loss of habitat, fisheries, pollution, and global change) (Council of the European Union 2007).
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However, those anthropogenic pressures are not uniformly distributed (Dekker 2003) and acts on
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specific fractions of the stock isolated in river catchments (Dekker 2000), with heterogeneous life-
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7
history traits because of the spatial phenotypic variability. This strong spatial heterogeneity of127
anthropogenic pressures affecting the eel population in Europe combined with this spatial
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phenotypic variability at both the distribution area and river catchment scales causes specific
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challenges for management, because it impairs our ability to assess the effect of anthropogenic
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pressures on the whole stock and to coordinate management actions (Dekker 2003, 2009).
131
Recently, a model called EvEel (evolutionary ecology-based model for eel) was developed to
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explore the contribution of adaptive phenotypic plasticity in the emergence of observed phenotypic
133
patterns: sex ratio, length at silvering, and habitat use (Drouineau et al. 2014). Assuming fitness
134
maximization, the model was able to mimic most observed patterns at both river catchment and
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distribution area scales. The result confirmed the probable role of adaptive phenotypic plasticity in
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response to environmental variability. However, recent findings demonstrated the existence of
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genetic differences in growth traits in a wide range of different habitats (Côté et al. 2009, 2014, 2015;
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Boivin et al. 2015). Building on these new results, we developed GenEveel, a new version of EvEel,
139
which introduces a bimodal growth distribution (fast and slow growers) for individuals, as observed
140
by Côté et al. (2015), and considers phenotypic plasticity in life-history traits and demographic
141
attributes as in EvEel. Because individuals have different intrinsic growth and mortality rates, they
142
can be favored differently among environments, opening the door to conditional habitat selection. In
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this study, we used GenEveel to test whether simultaneously considering genetically distinct
144
individuals and phenotypic plasticity improves model performance. Pattern orienting modelling was
145
used to detect the reproduced spatial patterns of EvEel and other patterns based on the distribution
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of the different types of individuals.
147
148
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3 Materials and methods
149
3.1 Model description
150
The model description follows the Overview, Design concepts, and Details (ODD) protocol
151
(Grimm et al. 2006, 2010):
152
3.1.1 Overview
153
3.1.1.1 Purpose
154
GenEveel is a model based on a former model called EvEel (Drouineau et al. 2014), but
155
includes a genetic component. It is an individual-based population model that predicts emergent life-
156
history spatial patterns depending on adaptive mechanisms and environmental heterogeneity.
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Emergent patterns can later be compared to observed spatial patterns in freshwater life stages of
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European eels in order to (i) confirm that observed phenotypic patterns can plausibly result from
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adaptive responses to environmental heterogeneity, (ii) validate that phenotypic plasticity for length
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at silvering, sex determination, habitat choice, and genetic polymorphism (slow growers and fast
161
growers) with conditional habitat selection can explain those patterns.
162
3.1.1.2 State variables and scales
163
Temporal scales: the model simulates a population generation. It has no sensu stricto time
164
steps, but rather successive events: sex-determination and habitat selection, survival, and growth
165
until maturation.
166
Entities and spatial scales: a Von Bertalanffy growth function is assumed for individual
167
growth. Each individual i is characterized by an intrinsic Brody growth coefficient Ki and a natural
168
mortality rate Mi. Based on Côté et al. (2015), who observed two clusters in growth rates, we build a
169
simple quantitative-genetic model assuming that growth is coded for by a single gene with two
170
variations. Therefore, we assumed that there are two types of individuals called (i) fast-growing
171
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individuals for which Ki = Kfast and Mi = Mfast and (ii) slow-growing individuals for which Ki = Kslow172
and Mi = Mslow. At the end of the simulation, individuals are characterized by a sex, length at
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silvering, corresponding fecundity (if female), position in the river catchment, and survival rate until
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silvering.
175
The river catchment environment was represented by a sequence of cells of the same size.
176
The first cell represents the river mouth, whereas the nth cell represents the source of the river.
177
Because it was observed that an individual grows faster downstream than upstream (Acou et al.
178
2003; Melià et al. 2006), we assumed that realized growth rate in a cell depends on both intrinsic
179
growth rate and position in the catchment (i.e., cell) (see submodel section). Realized natural
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mortalities depend both on individual intrinsic mortality rates, position of the cell in the catchment,
181
and number of individuals in the catchment (to mimic density-dependent mortality).
182
3.1.1.3 Process overview and scheduling
183
The model has two main steps. In a first step, individuals select their growth habitat (a cell in
184
the catchment) and determine a sex (male or female) one after another (random order). To do that,
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fitness is calculated for each combination of sex and cell (a quasi-Newton algorithm is used to
186
estimate the lengths at silvering that optimize female fitness in each cell). Individuals are assumed to
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select the combination with highest fitness given the choices made by former individuals. Once this
188
step is finished (i.e., all individuals have a growth habitat and sex), using the quasi-Newton algorithm
189
we estimated the optimal length at silvering for all females (males have a constant length at silvering)
190
given the positions of fishes from step 1, and then compute corresponding survival rates until
191
silvering and fecundity determination (Fig. 1). The process mentioned above is defined by the
192
computer algorithm (Figure 2):
193
(1) For each individual i:
194
- For each cell x:
195
· Compute πm(x) given positions of individuals {1,…,i-1}
196
10
· Compute f
f
Lsaxf π x,Ls
m given positions of individuals {1,…,i-1}
197
- Put individual and determine sex by selecting maximum values within f
f
Lsaxf π x,Ls
m and πm(x)
198
(2) For each individual i:
199
- For each cell x:
200
· if sex(i) = male
201
Ls(i) = Lsm
202
· else
203
Ls(i) = argL max (πf(x, Lsf)) given positions of individuals {1,…,n}
204
where fitness is defined in equations 9 and 10 for females and males respectively.
205
3.1.2 Design concept
206
3.1.2.1 Basic principles
207
Consistent with life-history theory and optimal foraging theory, the model uses an
208
optimization approach in which individuals “respond to choices” so as to select and fix the adaptive
209
traits, maximizing their expected fitness given their environment (Parker and Maynard Smith 1990;
210
McNamara and Houston 1992; Giske et al. 1998; Railsback and Harvey 2013).
211
3.1.2.2 Emergence
212
Using the pattern-oriented modelling approach (Grimm and Railsback 2012), GenEveel
213
compares predicted spatial patterns with those observed in real river catchments. Five emergent
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population spatial patterns were analyzed from the literature:
215
(i) higher density downstream than upstream
216
(ii) higher length at silvering upstream than downstream
217
(iii) male-biased sex ratio downstream and female-biased sex ratio upstream
218
11
(iv) more individuals characterized with the fast-growing genotype downstream than upstream,219
which was mainly characterized by the slow-growing genotype
220
(v) the phenotypic response led to faster growth rate downstream than upstream.
221
3.1.2.3 Adaptation
222
Individuals have three adaptive traits: sex-determination, length at silvering for females, and
223
choice of growth habitat (cell in the grid). These traits are assumed to maximize the predicted
224
objective function (i.e., the individual fitness).
225
3.1.2.4 Predictions
226
We assumed that individuals could perfectly predict expected fitness given previous choices
227
and could make the most appropriate choices.
228
3.1.2.5 Sensing
229
In the model, individuals are able to “sense” fitness, which was a function of a density-
230
dependent mortality and growth rate. In the real world, temperature and density would probably be
231
the proximal cues because natural mortality and growth rates are strongly influenced by temperature
232
(Bevacqua et al. 2011; Daverat et al. 2012).
233
3.1.2.6 Interaction
234
Interactions occurred through growth habitat selection, sex determination, and density-
235
dependent mortality.
236
3.1.2.7 Stochasticity
237
Stochasticity occurred at two levels. First, individuals were randomly affected by a slow-
238
growing genotype (Pr = 0.5) or by a fast-growing genotype (Pr = 0.5). Then stochasticity occurred in
239
the order of individuals for step 1.
240
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3.1.2.8 Observations241
Five spatial patterns were computed at the end of the simulation:
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(i) number of individuals per cell
243
(ii) mean length at silvering per cell
244
(iii) sex ratio (proportion of females) per cell
245
(iv) ratio of fast-growing genotype per cell
246
(v) phenotypic response of mean realized growth rate per cell.
247
These five patterns corresponded to five patterns available in the literature. Simulated patterns (i),
248
(iv), (v) was said to be consistent with the literature when a negative trend from downstream to
249
upstream was observed, whereas patterns (ii), (iii) were said to be consistent with the literature
250
when a positive trend was observed from downstream to upstream.
251
3.1.3 Details
252
3.1.3.1 Initialization
253
At the beginning of the simulation, the catchment was empty. N individuals were created and
254
attributed to the slow-growing or fast-growing genotype with probability 0.5 and had a length 7.5
255
cm. They had not yet entered the river catchment.
256
3.1.3.2 Input data
257
We tested the model using a reference simulation. Values of parameters were obtained from
258
the literature (Table 1). The outputs of the model were identified based on spatial patterns as
259
previously defined in Observations.
260
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3.1.3.3 Submodels261
Most of the submodels were similar to submodels from EvEel. Consequently, we provide
262
here only the novelties and the equations that are required for a better understanding of the model.
263
Further details are provided in Drouineau et al. (2014).
264
Growth and silvering
265
Growth rate was assumed the outcome of an intrinsic Brody growth coefficient (Ki), which is
266
modulated by an environmental effect. This combination resulted in a phenotypic growth rate.
267
Within the river, growth rates were significantly faster downstream than upstream (even for the
268
same individual). Therefore, we assumed that individual i would have a growth rate K(i, x) in cell x
269
given by:
270
(1)
K K
K n
K x r K + K r
=
Ki,x i,n i,1 i,n cauchit , γ
271
(2)
γ
x
= π
2 2 atan 1 γ x, cauchit
272
where rk defined the ratio between upstream and downstream growth rate, K(i, 1) is the growth rate
273
in cell 1, n is the total cells in the river catchment and cauchit was a mathematical function similar to
274
the sigmoid function, but which allowed asymmetrical patterns (by modifying the parameter γ) to
275
model, for example, a small brackish area in the downstream part of the catchment and a large
276
freshwater zone upstream.
277
Individual’s growth was simulated by a Von Bertalanffy function:
278
(3)
1 e Ki,x t t0 L
= x i, t,
279
Lwhere L(t, i, x) was the length at time t and L∞ and K(i, x), the Von Bertalanffy parameters in cell x for
280
individual i.
281
From this equation, we could calculate the time required to reach the length at silvering.
282
(4)
x i, L
Lg L x
i,
=K x
i, 1 log Ls
283
As14
where Lg was the length at recruitment and Ls(i, x) was the length at silvering, which was constant284
for males, and a fitness maximizing variable for females.
285
Survival
286
Mortality rate was assumed the result of three factors: density-dependence, intrinsic growth
287
rate, and Mi modulated by an environmental effect. Because natural mortality was sometimes
288
assumed to be smaller upstream than downstream (Moriarty 2003; Daverat and Tomás 2006), we
289
assumed that the instantaneous natural mortality without density-dependence in cell x for individual
290
i, M(i, x) was:
291
(5)
M M
M n
M x r M + M r
=
M i,x i,n i,1 i,n cauchit ,γ
292
where rm is the ratio between upstream and downstream instantaneous mortality rate and M(i, 1)
293
was the natural mortality in cell 1.
294
To account for the additional density-dependent mortality, we assumed that natural mortality
295
increased linearly with an intensity of density α as in EvEel:
296
(6) Md i,x =M i,x +N i,x α
297
where N was the number of competitors in cell x. An eel was assumed a competitor if it had an
298
intrinsic growth rate greater or equal to Ki. This corresponded to an asymmetric growth rate with
299
larger individuals harassing smaller individuals. The basis of this assumption was the intraspecific
300
competition, which leads to compete for limited resources between individuals of different sizes
301
(Francis 1983; Juanes et al. 2002).
302
Given equation (4) and this survival rate, we could calculate the probability of surviving until silvering
303
304
as:(7)
i, x K
x i, M x i, L
Lg
= L x i, x x i,
i, p
d Md
Ls e As
305
= Fitness
306
In any optimization model, an important component is the computation of the fitness.
307
Because sexes adopt different life strategies, and following Drouineau et al. (2014), we assumed sex-
308
15
specific fitness functions. Males were known to adopt a time minimizing strategy (Helfman et al.309
1987), with constant length at silvering. Therefore, male fitness was proportional to survival rate
310
until length at silvering. However, females follow a size-maximizing strategy in which length at
311
silvering was constrained by a trade-off between survival and fecundity (Helfman et al. 1987).
312
Consequently, we assumed that female fitness was the product of fecundity at an optimal length at
313
silvering (based on an allometric relationship, fecundity is assumed to be a power function of length)
314
multiplied by the probability of survival until this length at silvering. In the model, individuals were
315
assumed to determine their sex according to the relative potential male and female fitness. To make
316
fitness values comparable, we rescaled male fitness (which was the probability of survival) into an
317
expectation of egg production (the scale of female fitness). To do that, we multiplied the male
318
survival by a constant that would be similar to fertility. Hence, we had to specify a value for fertility
319
with an order of magnitude similar to fecundity. The first solution might be to fix the fertility value
320
equal to the fecundity of silver females having a length equal to male length at silvering. However,
321
with this solution, female fitness will always be greater (because females can optimize their length at
322
silvering). Consequently, fertility has to be slightly greater such that male fitness can be sometimes
323
be greater than female fitness (but not too much, to avoid male fitness always being superior). These
324
resulted in the following equations:
325
(8)
b
sf sf i,x = a +a L i,x L
fecundity 1
326
where a1, a and b are the parameters of the allometric relationship linking fecundity and female
327
length at silvering Lsf(i, x) (Andrello et al. 2011; Melia et al. 2006).
328
(9)
i,x
K x i, M
x i, L L
L L x i, L fecundity
= x π i,
f
sf g sf
f
329
(10)
i, x K
x i, M x i, L L
L fertility L
= x π i,
m
sm g m
330
16
3.2 Model exploration
331
3.2.1 Reference simulation
332
The reference simulation consisted of a simulation using parameter values in Table 1, i.e. the
333
best set of values found in the literature. After simulating this scenario, we analyzed the different
334
patterns. Mann-Kendall tests were implemented on each pattern to detect a monotonic upward or
335
downward trend of the variable of interest confirming the spatial patterns previously defined. The
336
correlation coefficient of this non-parametric test was denoted by τ.
337
3.2.2 Experimental design
338
Simulation design is a classical tool to explore complex models. Typically, the goal is to assess
339
the sensitivity of results to uncertain model parameters. We developed such an experimental design
340
to (i) assess the influence of uncertain parameters on the simulated patterns (Table 1) and (ii) derive
341
environmental and population dynamics for all the patterns that were correctly modelled.
342
Seventeen uncertain parameters were identified in the model (Table 1) and they were dispatched
343
into twelve groups: number of glass eel entering the catchment freshwater (N), parameters that
344
impact the male fitness (fertility and male length at silvering, Lsm), fast growing genotype (Kfast(i, 1)
345
and Mfast(i, 1)), slow-growing genotype (Kslow(i, 1) and Mslow(i, 1)), proportion of individuals that grow
346
slowly (propK), intensity of density-dependence (α), cells of river catchment (n), regression
347
coefficient from fecundity at length (b), asymptotic length (L∞), length at recruitment (Lg), ratio
348
between upstream and downstream instantaneous growth and mortality rates (rk and rm), and the
349
shape parameter of growth and mortality (γk and γm). Groups were composed of parameters that
350
have are assumed to influence the model in similar directions, a method called group-screening
351
(Kleijnen 1987). A low and high value was set for each parameter around the reference value, with
352
20% variation (Drouineau et al. 2006; Rougier et al. 2015), except for three sets of parameters:
353
fertility and Lsm(as a minimum value, fertility corresponded to the fecundity of a female with a length
354
17
at silvering equals to male length at silvering; otherwise, female fitness would always be superior to355
male fitness), and growth genotypes (to avoid overlap between them), where the range of variation
356
was less. We then conducted a fractional factorial design of resolution V (212-4 = 256 combinations).
357
This kind of orthogonal designs allows to explore main effects and first order interactions without
358
confusion. To account for model stochasticity, we conducted 10 replicates for each of the 256
359
combinations leading to 2560 simulations. The five patterns were calculated for each simulation
360
producing an output table with 2560 lines (one per simulation) and five columns containing the tau
361
value of the Mann-Kendall trend tests for each pattern (a negative tau value indicates a negative
362
trend from downstream to upstream while a positive tau indicates a positive trend from downstream
363
to upstream).
364 365
4 Results
366
4.1 Reference simulation
367
In the reference simulation, GenEveel mimicked the five spatial patterns at the catchment
368
scale (Fig. 3). Males were concentrated in the downstream section of the river where density was
369
higher (Helfman et al. 1987; Tesch 2003; Davey and Jellyman 2005). Fast growers preferentially
370
settled in downstream habitats, whereas slow growers tended to move upstream to avoid
371
competition (De Leo and Gatto 1995; Daverat et al. 2006, 2012; Drouineau et al. 2006; Edeline 2007;
372
Geffroy and Bardonnet 2012). Regarding mean length at silvering (for males and females), a smaller
373
size at maturity was simulated in the downstream section of the river, whereas larger lengths were
374
occurred gradually throughout the catchment (Vollestad 1992; Oliveira 1999).
375
The Mann-Kendall test confirmed that the five patterns were mimicked in the simulation.
376
More specifically, negative tau values confirmed a decreasing trend for density, ratio of fast growers
377
18
and mean realized growth rate; while positive tau values pointed to an increasing trend for ratio of378
females and mean length at silvering (Table 2).
379
4.2 Model exploration
380
For each combination, the 10 replicates provided the same results, confirming that the
381
patterns were not sensitive to stochasticity.
382
Interestingly, 310 simulations produced only females while 640 simulations produced only
383
males. Simulations with only females corresponded to simulation where density-dependence α, L∞
384
and the fecundity exponent b were simultaneously strong. Conversely, simulations with only males
385
corresponded to simulations with a low b and a low L∞. With only one sex, it was not possible to
386
calculate a spatial trend in sex ratio and with only males, it was not possible to calculate a trend of
387
length at silvering.
388
Two questions were addressed here. In a first time, we compared the five patterns to see
389
which of those patterns were frequently mimicked and which were less frequently mimicked. Then,
390
we compared the sensitivity of the model to each group of parameters. To quantify this sensitivity to
391
a group of parameters values, we compared the number of simulations that reproduce a given
392
pattern when the group had modality (-) with the number of simulations and when the group had
393
modality (+). A strong discrepancy indicated a high sensitivity to the group of parameters.
394
The Mann-Kendall tests of spatial patterns confirmed that the simulated patterns of
395
abundance, ratio of fast growers, and mean realized growth rate were consistent with the literature
396
in each of the 2560 combinations (Table 3). This result indicates that these model outputs do not
397
depend on parameters values in the parameter space considered. Consequently, the assumptions
398
about asymmetrical density-dependence and growth genotypes were enough to simulate catchment
399
colonization.
400
Regarding length at silvering pattern, patterns were consistent in 1300 simulations of the
401
1920 simulations for which it was possible to calculate a pattern (Table 3, Fig. 4 for several examples).
402
19
This meant that, in situations where some females were produced, the pattern was consistent in403
about 2/3 of the simulations. Length at silvering pattern appeared to be sensitive to most of the
404
parameters. The two most important were L∞ and b: consistent pattern were much more frequent
405
with a modality (+) (respectively 990 and 940 simulations) for these two parameters than with
406
modality (-) (respectively 310 and 360 simulations). This is not surprising since with modality (-) for
407
those parameters, the model produced only males in 640 simulations. Two other groups of
408
parameters had a strong influence: male fertility/ male length at silvering and density-dependence.
409
Consistent patterns were more frequent with low male fertility and length at silvering (800 with
410
modality (-) vs 500 with modality (+)), and with limited density dependence (810 with modality (-) vs
411
490 with modality (+)).
412
For the female ratio pattern, 130 simulations produced consistent patterns over the 1610
413
simulations for which it was possible to calculate a pattern (Table 3). This pattern was mostly
414
sensitive to four groups of parameters which correspond to the four most influential groups for the
415
pattern of length at silvering. Patterns were consistent only when male fertility/length at silvering
416
had modality (-) whereas Kslow/Mslow had modality (+). Moreover, consistent patterns were more
417
frequent when L∞ had a modality (-) and b a modality (+).
418
On the whole, 130 of the 2560 combinations produced results which were consistent for all
419
the five patterns (Table 4, Fig. 4 and Table S1). These 130 simulations corresponded exactly to the
420
130 simulations that produced consistent sex ratio patterns, demonstrating that this last pattern was
421
the more constraining (Fig. 5). Consequently, the interpretation regarding sensitive parameters was
422
similar.
423
To make a summary of those results: in situations where females’ fitness was favored
424
because of a strong L∞ or a strong b, i.e. a high fecundity, the model produced only females.
425
Conversely, when females were too penalised, model produced only males. Therefore, an equilibrium
426
was required between males and females fitnesses to mimic all patterns. The patterns in length at
427
silvering and sex ratio were the two most constraining patterns and were mainly sensitive to four
428
20
groups of patterns. These groups of parameters set the equilibrium between males and females429
fitnesses (male fertility and length at silvering, b and L∞) and the advantages between slow and fast
430
growers. Density-dependence was also important regarding the pattern on length at silvering. We
431
can observed that the five patterns were consistent mostly when slow growers and females were not
432
too penalized with respect to males and fast-growers.
433
Some of the patterns were indeed very constrained by model assumptions so it is hardly
434
surprising that they were mimicked by the model. For example, our constraints on mortality and
435
growth really constrained the distribution of fishes and probably the pattern of realized growth rates
436
in the catchment. However, those constraints were based on various observations in the literature
437
that have rarely been considered together to see if they make sense in a context of adaptive
438
response. We do not specify any constraints on the sex ratio, length at maturity and relationships
439
between sex ratio and slow/fast growers. Those results are really emerging patterns that are
440
consistent with the literature.
441 442
5 Discussion
443
5.1 Adaptation to environmental variability: phenotypic plasticity and
444
genetic polymorphism of European eel
445
The European eels, and more generally, temperate eels, display fascinating characteristics:
446
catadromy with a long larval drift, large distribution area with contrasted growth habitats, panmixia,
447
and strong phenotypic and tactic variability at different spatial scales. Consequently, this species is
448
relevant to explore adaptive mechanisms to environmental variability. Phenotypic plasticity has been
449
proposed as one such mechanism because of random mating and larval dispersal that prevent local
450
selection pressures to generate habitat-specific adaptations, or local adaptation, from one generation
451
to the next. Drouineau et al. (2014) developed the first model to explore the major role of
452
21
phenotypic plasticity in both life-history traits and tactical choices as an adaptive response to453
spatially structured environments and density dependence. However, recently Gagnaire et al. (2012),
454
Pujolar et al. (2014), Boivin et al. (2015), Côté et al. (2015) and Pavey et al. (2015) demonstrated the
455
existence of genetic differences correlated with the environment, suggesting that part of the
456
observed phenotypic variability had a genetic basis.
457
Based on the approach developed by Drouineau et al. (2014), the objective of this study was
458
to propose a model based on life-history theory and optimal foraging theory to explore the role of
459
both adaptive phenotypic plasticity and genetic polymorphism with genetic-dependent habitat
460
selection, in the emergence of phenotypic patterns. To that end, we used a pattern-oriented
461
modelling approach, as developed by Grimm et al. (1996). This kind of approach compared field
462
observed patterns to simulated patterns and postulated that those patterns are similar, the model is
463
likely to contain the mechanisms generating these patterns.
464
5.2 In which conditions were the patterns mimicked?
465
Similarly to Eveel, a main limitation of our approach was that it was based on a simulation
466
model with a pattern-oriented approach. Consequently, our results demonstrated that our
467
assumptions were plausible, but did not demonstrate that they were correct. Such a demonstration
468
would require demonstrating underlying mechanisms, for example by conducting complementary
469
controlled experiments.
470
We built a full experimental design to explore the model. This type of approach is classical in
471
complex model exploration (de Castro et al. 2001; Faivre et al. 2013). For example, in the context of
472
sensitivity analysis of complex simulation models (Drouineau et al. 2006). Our exploration goals were
473
to generate simulations from the parameter space and analyze the qualitative differences in the
474
model output to (i) study the impact of parameters on the model output, (ii) determine which
475
parameters were the most important, and (iii) identify the combinations of parameters required to
476
22
mimic all observed spatial patterns. In this study, 17 parameters grouped in 12 set of parameters,477
were chosen to define the region of the parameter space where all spatial patterns were reproduced.
478
To assess the influence of stochasticity, we made 10 replicates per combination. This can
479
appear limited, however, it was impossible to increase the number of simulations and we preferred
480
to have a better exploration of uncertainty due to uncertain parameters rather than on stochasticity
481
which is rather limited in our model. Stochasticity occurs during the initialization process when
482
randomly building slow or fast value with a given probability. This corresponds to a binomial
483
distribution which has, given the large number of individuals, a very small variance. Stochasticity also
484
occurs in the order of individuals for step 1, but this is closely linked to the previous process and
485
consequently also has a limited variability. This limited effect of stochasticity was confirmed by our
486
results since patterns per combination were always consistent among replicates (Fig. 4 and 5).
487
One hundred thirty simulations among the 2560 mimicked the five spatial patterns. The
488
fourth pattern stated that fast growers and slow growers had different spatial distributions. Fulfilling
489
this pattern demonstrated that genetically different individuals have different habitat selection
490
strategies to maximize their respective fitnesses. Consequently, fulfilling the five patterns suggested
491
that, at least in certain conditions, genotype-dependent habitat selection and phenotypic plasticity
492
could explain observed phenotypic patterns. The level of sensitivity was variable among groups of
493
parameters, but four main groups of parameters were crucial: males’ fertility and length at silvering,
494
growth and mortality rates of slow growers, fecundity, and L∞. Density-dependence was also an
495
important parameter regarding length at silvering. In summary, the patterns were mimicked in
496
simulations with dominants and dominated but when dominated individuals, mainly females, were
497
not too penalized with respect to dominants, mainly males.
498
Regarding the spatial patterns, higher density, higher proportions of fast growers, and faster
499
growth rates in downstream regions were mimicked for all combinations of parameters. This
500
suggested that in the range of variation considered, none of the parameters had effects on model
501
outputs. This probably means that the gradient in environmental conditions and the population
502
23
dynamics in the model were sufficient to reproduce these patterns, regardless of the competitive503
advantage of fast growers with respect to slow growers, confirming that phenotypic plasticity plays
504
an important role in environmentally induced changes in life-history traits and demographic
505
attributes. Concerning the two other patterns (sex ratio and length at silvering), additional
506
hypotheses are needed regarding competition and genetic polymorphism. They were fulfilled in
507
conditions of weak competition and when growth differences were not too strong between the two
508
genotypes.
509
5.3 Consequences of intra-specific competition
510
In our model, we assumed the existence of asymmetrical density dependence between fast
511
and slow growers. We assumed that smaller individuals would avoid engaging in competition with
512
larger ones (regardless of sex) and would consequently be more affected by density dependence.
513
This assumption seems ecologically realistic. Asymmetrical density dependence has been observed in
514
plants (Weiner 1990), insects (Varley et al. 1973), and fish (DingsØr et al. 2007). Intraspecific
515
competition is a very common mechanism of density dependence, favoring large body size in fishes
516
(Francis 1983; Juanes et al. 2002). In anguillid eels, this may be manifested through agonistic
517
interactions (Knights 1987; Bardonnet et al. 2005), including cannibalism (Edeline and Elie 2004).
518
Such behaviors have been observed in yellow eels under artificial rearing conditions (Peters et al.
519
1980; Degani and Levanon 1983; Knights 1987).
520
We modelled this asymmetric competition by specifying different levels of density-
521
dependent mortality for slow and fast growers. Interestingly, the spatial patterns were still
522
reproduced when setting these parameters to a similar value (not presented here). Indeed, even with
523
similar intensity of density dependence, slow growers needed more time to reach their length at
524
silvering and consequently, suffered competition longer. Thus, even if competition has the same
525
impact on instantaneous mortality rates of slow and fast-growers, density dependence produces
526
asymmetric impacts on their respective fitness. In EvEel, Drouineau et al. (2014) assumed the
527
24
existence of asymmetric competition between males and females, with females being more affected528
by competition. Interestingly, we observed in our results that females had a higher proportion of
529
slow growers than males. This means that the gender-based asymmetry proposed by Drouineau et al.
530
(2014) may be an indirect result of an asymmetry between two genetically distinct types of
531
individuals with respect to growth.
532
The asymmetric competition implies that fitness of individuals having a given growth
533
genotype depends on the number of individuals having the other growth genotype, which may lead
534
to frequency-dependent selection (Heino et al. 1998). This has several implications. In the model, we
535
assumed that individual fitness corresponded to the lifetime reproductive success called R0, and that
536
this fitness is maximized. However, in a frequency-dependent selection context (i) natural selection
537
does not necessarily lead in fitness maximization (Mylius and Diekmann 1995; Metz et al. 2008), and
538
(ii) fitness may need to be defined as an invasion criterion (Metz et al. 1992). Even when fitness
539
maximization applies, r, the population growth rate, may be a more appropriate measure of fitness
540
than R0 depending on how density-dependence acts (Mylius and Diekmann 1995). To ensure that
541
our assumptions about fitness definition and maximization were valid would require a multi-
542
generational model at the scale of the population distribution area. This would allow computing
543
fitness for the whole life-cycle across all potential habitat types of the distribution area while
544
accounting for population structure in terms of genotypes or clusters. At this point, it would be
545
interesting to explore the heritability of the different traits and the intra-generational spatially
546
varying selection, a mechanism suggested by the SNP differences according to latitude (Pujolar et al.
547
2011; Gagnaire et al. 2012; Ulrik et al. 2014).
548
This was not possible because of difficulties to develop a whole life-cycle model. More
549
specifically, the fractal dimension of the eel population makes it very difficult to develop a population
550
dynamics model for the continental phase at the distribution area scale. Moreover, such a model
551
would require the use of stock-recruitment relationships, which is very difficult for the European eels
552
because of insufficient data, long larval drift, and different recruitment trends through the
553
25
distribution area. In this context, we had to use intra-generational model and a R0 fitness function,554
restricted to a single catchment and a portion of the whole life-cycle, and to postulate that this R0
555
was maximized.
556
5.4 Reinterpreting the time-minimizing and size-maximizing strategies
557
To summarize the results for combinations of parameters that mimicked observed patterns,
558
we observed a high proportion of individuals, mainly fast growers, in the downstream environment,
559
which corresponded to marine or brackish water. These individuals were mainly males with a
560
constant length at silvering. In upstream areas, we found mainly slow growers, primarily females with
561
higher length at silvering. This can aid in the reinterpretation of gender difference in life tactics (i.e.,
562
males with a time-maximizing strategy and females with a size-maximizing strategy). Our results
563
suggest that these tactics were possibly based on the existence of two genotypes for growth. Fast
564
growers grow fast but suffer higher mortality (because they inhabit downstream habitats with higher
565
mortality and density); a time-minimizing strategy is suitable for them. Slow growers grow slowly but
566
suffer lower mortality, consequently they can stay longer in continental habitats, and a size-
567
maximizing strategy is suitable for them.
568
Another interesting question is whether cues are used by individuals to select their growth
569
habitat. In the model, individuals were omnipotent and omniscient: they were able to assess the
570
potential fitness in each cell and move in the most suitable cell. This would mean that they were able
571
to assess the natural mortality, growth rate, and density in each cell. Drouineau et al. (2014)
572
suggested that temperature might be one of the main proximal cue used by individuals to assess the
573
suitability. Regarding density-dependence, reaction to aggressiveness (Geffroy and Bardonnet, 2012)
574
or cons-specific odors (Schmucker et al. 2016) were observed on growth and propensity to migrate.
575
Vélez-Espino and Koops (2010) also revealed temperature as main factor explaining variation in life-
576
history traits. Our model suggested that density in various habitats was also probably a main cue,
577
especially for slow growers, which tended to minimize competition.
